JHEP07(2019)140
the large scale concept, instead of temperature. Possible interactions where theorized on
in [7], but those are not central to the present analysis. Importantly, a particle property
corresponding to time might be as indirectly connected to time as kinetic energy is to
temperature, and to identify what the quantum properties really are is a challenge we will
only touch upon in this article.
An example of possible ‘insulation’ in space-time would be new physics at event hori-
zons, as suggested in the firewall and fuzzball conjectures. Our current analysis aims at
considering an interaction origin and the effects thereof, to see if such a scenario could be
consistent, and if observable physics far away from event horizons support, contradict or
is indifferent to the scenario.
1.2 The model, at the quantum level
At the quantum level, the basic suggestion is to replace the metric tensor of general relativ-
ity (in its role of giving rise to ds
2
) with interactions between pairs of quantum particles,
including (and heavily reliant on) quantum fluctuations. For a connection to the metric, we
look to rates of information exchange. The metric tensor can straightforwardly be reinter-
preted as describing a connectivity between quantum particles in terms of a frequency, with
length through dl ∼ c/f, and relative passage of time for each quantum particle through
its total rate of interaction, with dt ∼ 1/f
t
. In a diagonal metric, we have hc
2
f
2
t
i = −g
tt
.
However, as frequencies (f
t
, f) are merely dummy notations derived from the connection
to the classical properties, not necessarily inherent to the quantum model (compare to E
k
and T ). At the quantum level, (f
t
, f) can correspond to some particle energies (or internal
properties) not directly related to time or space. One might e.g. consider a scenario where
the f
t
of a particle contributes to time in the sense of how the kinetic energy of a particle
contributes to the temperature in its surroundings; describing (in some sense) a likelihood
of interacting.
An equilibrating process is assumed to exist, so that gradients are suppressed, and to
begin with the points of reference can be thought of as on a lattice. We discuss this ansatz
further in section 3. Right here the argument is that an average over interactions such as
these can give rise to an effective metric tensor while the quantum physics is allowed to be
decidedly different from a background scenario.
The quantum interactions are the object of investigation in section 3. We look at how
they are restricted by properties of flat space-time (including information exchange effects
at the classical level) and by the metric tensor. We give some comments on what to expect
with curvature, and in the near-horizon region, but restrictions from and quantum effects
associated with curvature require analyses beyond those given in the present text.
1.3 The model, at the classical level
An origin of space-time in information exchange (interactions) would have consequences at
the classical level beyond what is described by general relativity, and not limited to event
horizons or curvature. Note that while the emergent theory in classically safe regions (far
away from not only high curvature, but even curvature giving rise to event horizons) must
– 4 –
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